Abstract
In this paper, we first introduce a cyclic generalized contraction map in metric spaces and give an existence result for a best proximity point of such mappings in the setting of a uniformly convex Banach space. Then we give an existence and uniqueness best proximity point theorem for non-self proximal generalized contractions. Moreover, an algorithm is exhibited to determine such a unique best proximity point. Some examples are also given to support our main results. Our results extend and improve certain recent results in the literature.